Sequential inference for dynamically evolving groups of objects

IEEE Trans. Signal Process.

2021

The Non-homogeneous Poisson process is a point process with time-varying intensity across its domain, the use of which arises in numerous areas in signal processing and machine learning. However, applications are largely limited by the intractable likelihood function and the high computational cost of existing inference schemes. We present a sequential inference framework that utilises generative Poisson data and sequential Markov Chain Monte Carlo (SMCMC) algorithm to enable online inference in various applications. The proposed model is compared to competing methods on synthetic datasets and tested with real-world financial data.

Section: Sequential Inferencementioning

confidence: 99%

Sequential Inference Methods for Non-Homogeneous Poisson Processes With State-Space Prior

IEEE Trans. Signal Process.

2021

“…Instead, we address this high-dimensional proposal with a SMCMC algorithm which targets sequentially the joint distributions of Eq. (17), using both local and global Metropolis-Hastings (MH) accept-reject moves instead of importance sampling or resampling [20], [14], [21], [22].…”

Section: Sequential Inferencementioning

confidence: 99%

Sequential Inference Methods for Non-Homogeneous Poisson Processes with State-Space Prior

2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

2018

Self Cite

The non-homogeneous Poisson process provides a generalised framework for the modelling of random point data by allowing the intensity of point generation to vary across its domain of interest (time or space). The use of non-homogeneous Poisson processes have arisen in many areas of signal processing and machine learning, but application is still largely limited by its intractable likelihood function and the lack of computationally efficient inference schemes, although some methods do exist for the batch data case. In this paper, we propose for the first time a sequential framework for intensity inference which combines the non-homogeneous model of Poisson data with continuoustime state-space models for their time-varying intensity. This approach enables us to design efficient online inference schemes, for which we propose a novel sequential Markov chain Monte Carlo (SMCMC) algorithm, as is demanded by many applications where point data arrive sequentially and decisions need to be made with low latency. The proposed approach is compared with competing methods on synthetic datasets and tested with highfrequency financial order book data, showing in general improved performance and better computational efficiency than the main batch-based competitor algorithm, and better performance than a simple baseline kernel estimation scheme.

“…Reversible jump MCMC methods must be used to handle the varying number of notes. See [7] for details of similar schemes for tracking and finance applications, [10] for general information about MCMC, and [11] for details of the reversible jump MCMC framework. Our implementation proceeds as shown in Algorithm 1.…”

Section: Sequential Mcmcmentioning

confidence: 99%

“…A dynamical model for these parameters over time frames then completes a Bayesian spatio-temporal state space model. Inference in this model is carried out using a specially modified version of the sequential MCMC algorithm [7], in which information about the previous frame is collapsed onto a single univariate marginal representation of the multipitch estimation.…”

Section: Introductionmentioning

confidence: 99%

Point process MCMC for sequential music transcription

Bunch

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

2011

In this paper, models and algorithms are presented for transcription of pitch and timings in polyphonic music extracts, focusing on the algorithm details of the sequential Markov chain Monte Carlo (MCMC) inference techniques used. The data are decomposed frame-wise into the frequency domain, where a Poisson point process model is used to write a polyphonic pitch likelihood function. A dynamical model is then used to link notes between frames. Inference in the model is carried out via Bayesian filtering using a sequential MCMC algorithm. The filtering procedure is sub-optimal, using some novel assumptions to render the task computationally tractable for large numbers of notes. Initial results with guitar music, both laboratory test data and commercial extracts, show promising performance.